Even though in this work we will not discuss the construction of the quantized calculus for
the magnetic Fredholm module, we will use the notation (REF ) to prove the so called
first Connes' formula according to the name introduced by Bellissard et al. for [1]}. It is worth pointing out that the first Connes' formula as proved in [1]} works only for the discrete magnetic algebra. In contrast, the proof that we will provide here concerns with the continuous case.
